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On Stability and Boundedness of Solutions of a Certain Non-autonomous Third-order Functional Differential Equation with Multiple Deviating Arguments

Автор(ы):

Mohamed A. Abdel-Razek

Department of Mathematics, Faculty of Science, Assiut University,
Assiut 71516, Egypt

abdel_razek555@yahoo.com

Ayman M. Mahmoud

Department of Mathematics, Faculty of Science,
New Valley University, El-Khargah 72511, Egypt

math_ayman27@yahoo.com

Doaa A. M. Bakhit

Department of Mathematics, Faculty of Science,
New Valley University, El-Khargah 72511, Egypt

doaa_math90@yahoo.com

Аннотация:

This paper investigates the explicit criteria of the stability of the zero solution and the boundedness of all solutions for a certain non-autonomous third-order functional differential equation with multiple deviating arguments. To study the stability of the zero solution we construct the Lyapunov functional. The Gronwall-Reid-Bellman inequality is employed to establish the boundedness of all solutions of the addressing model. This study includes and improves some related results existing in the relevant literature. For illustration, two examples are given.

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Ссылки:

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